A393227 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^2) / (1 - x)^3.

1, 1, 4, 15, 68, 365, 2215, 14917, 110324, 887232, 7692852, 71431239, 706389705, 7404870499, 81949655191, 954124880754, 11650772679964, 148804052320029, 1983050788356644, 27515009940760592, 396709919909663826, 5933004526233997409, 91891268337714271137, 1471741514111153388248

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+k+1,n-k-1) * a(k).

Mathematica

nmax = 23; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - x)^2]/(1 - x)^3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + k + 1, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 23}]

Crossrefs

Cf. A000110, A040027, A045501, A125273, A125274, A351813, A351816, A393228.

Sequence in context: A250886 A391060 A055732 * A125062 A039625 A020020

Adjacent sequences: A393224 A393225 A393226 * A393228 A393229 A393230

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 06 2026

Status

approved